A306524 Number of permutations p of [n] having at least one index i with |p(i)-i| = 2.

0, 0, 0, 3, 15, 86, 544, 3934, 32079, 292509, 2952702, 32712087, 394749367, 5155010088, 72440184064, 1090017765544, 17486996858151, 297965879586295, 5374189975316350, 102290550351854445, 2049025241258716927, 43089888746430771294, 949172134240270646352

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..450

Wikipedia, Permutation

Formula

a(n) = n! - A306523(n).

Example

a(3) = 3: 231, 312, 321.
a(4) = 15: 1342, 1423, 1432, 2314, 2413, 2431, 3124, 3142, 3214, 3241, 3412, 3421, 4132, 4213, 4312.

Mathematica

T[n_, k_] := n! - Permanent[Table[If[Abs[i-j] == k, 0, 1], {i, 1, n}, {j, 1, n}]];
a[n_] := If[n == 0, 0, T[n, 2]];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 23}] (* Jean-François Alcover, Oct 31 2021, after Alois P. Heinz in A306506 *)

Crossrefs

Column k=2 of A306506.

Cf. A000142, A306523.

Sequence in context: A093615 A191148 A001931 * A355097 A180677 A220875

Adjacent sequences: A306521 A306522 A306523 * A306525 A306526 A306527

Keyword

nonn

Author

Alois P. Heinz, Feb 21 2019

Status

approved